Extremes

, Volume 15, Issue 4, pp 463–489 | Cite as

Adaptive estimation of heavy right tails: resampling-based methods in action

  • M. Ivette Gomes
  • Fernanda Figueiredo
  • M. Manuela Neves
Article

Abstract

In this paper, we discuss an algorithm for the adaptive estimation of a positive extreme value index, γ, the primary parameter in Statistics of Extremes. Apart from the classical extreme value index estimators, we suggest the consideration of associated second-order corrected-bias estimators, and propose the use of resampling-based computer-intensive methods for an asymptotically consistent choice of the thresholds to use in the adaptive estimation of γ. The algorithm is described for a classical γ-estimator and associated corrected-bias estimator, but it can work similarly for the estimation of other parameters of extreme events, like a high quantile, the probability of exceedance or the return period of a high level.

Keywords

Statistics of extremes Semi-parametric estimation Resampling-based methodology 

AMS 2000 Subject Classifications

Primary—62G32 62E20; Secondary—65C05 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • M. Ivette Gomes
    • 1
  • Fernanda Figueiredo
    • 2
  • M. Manuela Neves
    • 3
  1. 1.Universidade de Lisboa, FCUL, DEIO and CEAULLisboaPortugal
  2. 2.Faculdade de Economia and CEAULUniversidade do PortoPortoPortugal
  3. 3.Instituto Superior de Agronomia and CEAULUniversidade Técnica de LisboaLisboaPortugal

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